Design and convergence analysis of some implicit inertial methods for quasi-variational inequalities via the Wiener–Hopf equations

Abstract

In this work, various implicit methods are proposed solve the quasi-variational inequality problem. It is well known that Tseng's algorithm developed by Thong replaces the high-precision step size. To avoid this shortcoming, several new forward-backward inertial methods are proposed by adopting the technique of the Wiener–Hopf equation. The convergence of the algorithms is investigated under suitable conditions on the operators and parameters involved. The results reported in the paper are substantial improvements with respect to previous works available in the literature. Some computational simulations obtained by using a computational implementation of our techniques show that some of the present algorithms are able to approximate the optimum of standard problems faster than some algorithms already available in the specialized literature.